Aontú has brought forward a motion in the Dáil seeking to reform the presidential election process.
It has called for the threshold on nominations to be lowered to ensure more candidates, and for Irish citizens on both sides of the border to vote in presidential elections.
The party also asked for Áras an Uachtaráin to be subject to Freedom of Information requests.
Party leader Peadar Tóibín said it would bring "one of the biggest reforms" to the Presidential Election process in the history of the State.
He said the motion would tackle the "shocking democratic deficit" in the Presidential Election.
He said "so many people" are angry at the "Presidential Election farce" that is enfolding.
People feel "locked out" out of the election campaign, according to Mr Toibín.
He said the party's motion would "open up" the Presidential Election nomination process to ensure a larger number of candidates "more representative of the people" would be able to participate in an election campaign.
He said it would allow for the "competition of ideas where the best ideas would percolate to the top".
He said the Presidential Election has "an extremely high threshold" - that is "giving the power to the Oireachtas and the councils who decide "who even gets on the ballot".
"Let the people pick the President," said Mr Toibín.
He said the polls show that many people are not likely to vote and a "significant" number will spoil their vote.
"One of the polls show that Maria Steen would have achieved 22% of the actual vote in the election, yet she has not been allowed onto that ballot," said Mr Toibín.
He said this should be a "wake-up" call and said people are "disengaging" from the Presidential Election.
Independent Ireland supported the motion.
Independent Ireland leader Michael Collins said he feared Friday's election would see one of the lowest ever turnouts as people have "turned off".
In response, the Minister for Housing, Local Government and Heritage said the Government is not opposing the motion.
James Browne said extending voting rights to Northern Ireland or to change the Presidential Election nomination process would require referendums.
He said the office of Áras an Uachtaráin is subject to a separate and discrete vote of its own and is subject to audit from the Comptroller and Auditor General.
Its expenditure is subject to examination by the Public Accounts Committee.
Mr Browne said making the office subject to FOIs "may not outweigh the potential risks of ensuring the independence" of the Presidency.
